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Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

28080 questions
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Bivariate Normal Manipulation

I do not understand the section of the solution highlighted.
usainlightning
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Exchangeability of a Joint PDF

I'm wondering why the exchangeability of the bivariate normal pdf, allows me to immediately write down the distribution of Y2, having found that of Y1.
usainlightning
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When determining the bounds of integration to calculate the marginal density of X, why are they |x| to infinity?

I'm having trouble seeing why the bounds of integration used to calculate the marginal density of $X$ aren't $0 < y < \infty$. Here's the problem: $f(x,y) = \frac{1}{8}(y^2 + x^2)e^{-y}$ where $-y \leq x \leq y$, $0 < y < \infty$ Find the…
Mlagma
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Which probability distribution is this?

Suppose we draw a number $x$ uniformly distributed on $(0,1)$, what is then the following distribution. Furthermore, calculate $F(y)$ and $f(y)$. $$y = \dfrac{x}{1-x}$$ This is a question I came across. Looks very simple, but I just simply do not…
onimoni
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Maximum Likelihood from observed values

Give IID Data Samples $X_n = $ {$x_1, x_2, ..., x_n$} generated from a uniform distribution $U(x|0,\theta)$. $p(x|\theta) = U(x|0,θ) = ${$ \frac{1}{\theta}$ for $0 \leq x \leq θ$ and $0$ otherwise}. Now assuming $X_2 = [1, 3, 2, 4]$ have been…
user136542
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Probability densitiy of $\cos x$

If $x$ is of Uniform distribution between $0$ and $2\pi$, what is the probability of $\cos(x)$ having a value between $-0.5$ and $0.5$? I tried transformation, but I somehow get $1/6$ but it seems to be $1/3$. Greetings
user137213
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Test hypothesis

I have a pre intervention group of $80$ patients and a post intervention group of $80$ patients. I need to know if there is a difference between the percentages of the pre group and post. example, after the intervention, there was an $80\%$ increase…
Awais
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Probability distribution of a function of a random variable $P(y(x))$

Do you have an idea about how to prove the following? (references will be useful) Let $x$ a random variable with probability distribution $ρ(x)$, and $y=f(x)$ another random variable, then the probability distribution of $y$ is $$P(y)=\int \rho…
Ana S. H.
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(not asympotic) relation between hypergeometric and binomial distribution

Let $H$ be a random variable with hypergeometric distribution of parameters $n,h,r$ (that is $n$ is the total number of elements, $h$ elements are white and I choose $r$ elements). Let $B$ be a random variable with binomial distribution of…
Clara
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probability chi-square distribution

If X and Y are the marks scored by a student in mid-sem and end-sem independently. Assume mid-sem marks and end-sem marks follow 2 distribution with degrees of freedom 3 and 6. A student is evaluated only on these two exams and the student passes if…
robin
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Probability of matching

Let the alphabet from which characters are taken is of size 'k' If a string S1 contains 'n' characters String S2 contains 'm' characters (m << n) What is the probability of a character in S1 is equal to a character in S2 ?
hanugm
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find a CDF for a liner transformation for indipendent random variable

given that $X_1 \sim U[-2,1]. X_2=0.5e^{-|t|}, -\infty
user107761
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Which distribution would fit this binomial type series of events?

We have arbitrarily many lottery scratch-n-win tickets Each ticket has a $p=0.1\%$ chance to win 1 prize (a success event) Scenario A, Scratch n tickets and record the number of prizes won $X$: From the binomial distribution, $X$ will have a mean…
gregsan
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transfer function over a uniform distribution to generate a two-fold variation, but result is also s uniform distribution

I think, I am stuck at a transformation problem where I believe there is a solution, but I don't know what it is. I have uniform distribution $u_1(x) = \frac{1}{b - a}$, where $b=-1$ and $a=1$, and want to utilize it to generate two fold variation…
Hiren
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Find a the density function for Y(1) = min(Y1, Y2, . . . , Yn).

Suppose that the length of time Y it takes a worker to complete a certain task has the probability density function given by $f(y)=\begin{cases} e^{-(y-\theta)} &, y>\theta\\ 0 & ,elsewhere \end{cases}$ where θ is a positive constant that represents…
afsdf dfsaf
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